Question

15. Quick Traps manufactures an innovative mouse trap. Sales this year are $280,000. The company expects its sales to go up to $440,000 in six years. What is the expected growth rate in sales for this firm? A) 7.82% B) 8.36% C) 5.71% D) 9.30% 16. Madison purchased a new car for $29,000. She was allowed $3,000 for her trade in and financed the remainder over 48 months of 4.2% per year. How much is her monthly payment? A) $407.45 B) $451.58 C) $589.39 D) $444.16 17. The expected return for Stock Z is 17 percent. If we know the following information about Stock Z, then what return will it produce in the Lukewarm state of the world? Return Probability 0.1 0.30 0.50 0.20 0.30 A) B) C) D) Poor Lukewarm Dynamite! 20% 30% 16% 22% 18. You have invested $16,000 of your portfolio in a stock with expected return of 8 percent and $24,000 in a stock with an expected return of 13 percent. What is the expected return of your portfolio? A) 15.6% B) 13.2% C) 12.4% D) 11.0%

Answer 1

15.

Sales this year = S₁ = 280000

Sales after 6 years = S₆ = 440000

Growth Rate = (S₆/S₁)^1/6 - 1 = (440000/280000)^1/6 - 1 = 0.0782 or 7.82%

16.

Value of new car = $29000

Trade in value = $3000

Hence, Loan Amount = P = 29000 - 3000 = $26000

Interest Rate = 4.75% or 0.042/12 monthly

Number of payment periods = n = 48 months

Let monthly payments made be X

Hence, the sum of present value of monthly payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

Hence, Monthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 26000*( 0.042/12)*(1+ 0.042/12)⁴⁸/((1+ 0.042/12)⁴⁸-1) = $589.39

17.

Let lukewarm return be x

Expected Return = ΣP_iR_i , where P is the probability and R is the return for state i

Given, Expected return = 17%

=> 0.17 = 0.1*0.30 + x*0.50 + 0.30*0.20

=> x = (0.17 - 0.1*0.30 - 0.30*0.20)/0.50 = 0.16 or 16%

18.

Total Investment = 16000 + 24000 = $40000

Proportion invested in Stock 1 = 16000/40000 = 0.40

Proportion invested in Stock 2 = 24000/40000 = 0.60

Return for Stock 1 = 8%

Return for Stock 2 = 13%

Hence, Expected Return = ΣReturn * Proportion = 0.40*8 + 0.60*13 = 11%